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Soft Computing

, Volume 23, Issue 22, pp 11389–11398 | Cite as

Extensions of a tight function and their continuity in quantum logic

  • Mona Khare
  • Pratibha PandeyEmail author
Foundations
  • 45 Downloads

Abstract

In the present paper, a new variation of a nonnegative real-valued function \(\rho \) defined on a subfamily of a quantum logic P is proposed, and the notion of tightness of \(\rho \) is studied. Various crucial results are proved, and subsequently we have obtained extensions, viz. f-extension, \(\delta \)-extension and \(\sigma \)-extension of a tight function \(\rho ;\) continuity of extensions of \(\rho \) with respect to an approximating family in P is discussed.

Keywords

Orthomodular lattices Continuity Tight functions Approximating families 

Notes

Acknowledgements

The authors are grateful to the anonymous referees for their valuable suggestions toward the improvement of the paper.

Funding

The second author acknowledges with gratitude the financial support by Department of Science and Technology (DST), New Delhi, India, under INSPIRE fellowship No. IF160721.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants (co-author) included in the study.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AllahabadAllahabadIndia

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